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On the variational principles for partial differential equations. (English) Zbl 0675.35003

The paper deals with the inverse problem for partial differential equations. For a given partial differential equation \(\epsilon (x^ i,u(x^ i),D_{j_ 1} u_ 1,...,D_{j_ 1}...D_{j_ r} u)=0,\) an operator A: \(X\to X^*\) is defined.
The author uses a modified theory of potential operators as given by Vanderbauwhede and formulates a criterion for the operator A to be the potential operator. Finally, the author constructs explicit formulae for the potential of the operator A.
Reviewer: I.Horová

MSC:

35A15 Variational methods applied to PDEs
35R30 Inverse problems for PDEs
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